Predefined-Time Noise Immunity ZNN Model for Dynamic Quaternion Least Squares Problem and Application to Synchronization of Hyperchaotic Systems

Currently, there is a dearth of algorithms for solving the dynamic quaternion least squares problem (DQLSP), and the traditional numerical methods cannot solve dynamic problems effectively. To solve the DQLSP, a predefined-time noise immunity ZNN (PTNIZNN) model and a novel activation function are presented, building upon the traditional zeroing neural network (ZNN) model. The convergence time (CT) of the PTNIZNN model is only related to a predefined-time (PT) parameter, which makes it simpler to adjust the CT than the prior fixed-time convergence ZNN model. It is proved via mathematical deductive reasoning that the PT convergence and noise immunity of the PTNIZNN model hold when solving the DQLSP. In addition, a numerical example is given to demonstrate the correctness of mathematical deductive reasoning and the advantages of the PTNIZNN model. Finally, according to the design scheme of the PTNIZNN model, a new controller is designed to achieve the synchronization of the hyperchaotic Lorenz systems and applied to image encryption.